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Regione 3
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Regione 3

 


Equazioni di base

Le equazioni di base relative a questa regione coincidono con l’equazione fondamentale dell’energia libera di Helmholtz f. Questa equazione espressa in forma adimensionale, Φ=f /(RT), si legge: 

 (28)

 

dove ρ=ρ/ρ* , t=T*/T con ρ*=ρc, T*=Tc e R, Tc e ρc ricavati dalle equazioni (1) e (2)
I coefficenti ni e gli esponenti Ii e Ji sono elencati nella seguente tabella 30. 

TABELLA 30
Valori dei coefficenti e degli esponenti della equazione adimensionale dell’energia libera di Helmholtz relativi alla regione 3 come da eq. (28)

i
I i
Ji
ni
1
0
0
0.106 580 700 285 13 x 101
2
0
0
-0.157 328 452 902 39 x 102
3
0
1
0.029 443 969 743 07 x 102
4
0
2
-0.768 677 078 787 16 x 101
5
0
7
0.261 859 477 879 54 x 101
6
0
10
-0.280 807 811 486 20 x 101
7
0
12
0.120 533 696 965 17 x 101
8
0
23
-0.845 668 128 125 02 x 10-2
9
1
2
-0.126 543 154 777 14 x 101
10
1
6
-0.115 244 078 066 81 x 101
11
1
15
0.885 210 439 843 18
12
1
17
-0.642 077 651 816 07
13
2
0
0.384 934 601 866 71
14
2
2
-0.852 147 088 242 06
15
2
6
0.489 722 815 418 77 x 101
16
2
7
-0.305 026 172 569 65 x 10-1
17
2
22
0.394 205 368 791 54 x 10-1
18
2
26
0.125 584 084 243 08
19
3
0
-0.279 993 296 987 10
20
3
2
0.138 997 995 694 60x 101
21
3
4
-0.201 899 150 235 70 x 101
22
3
16
-0.821 476 371 739 63 x 10-2
23
3
26
-0.475 960 357 349 23
24
4
0
0.439 840 744 735 00 x 10-1
25
4
2
-0.444 764 354 287 39
26
4
4
0.905 720 707 197 33
27
4
26
0.705 224 500 879 67
28
5
1
0.107 705 126 263 32
29
5
3
-0.329 136 232 589 54
30
5
26
-0.508 710 620 411 58
31
6
0
-0.221 754 008 730 96 x 10-1
32
6
2
0.942 607 516 650 92 x 10-1
33
6
26
0.164 362 784 479 61
34
7
2
-0.135 033 722 413 48 x 10-1
35
8
26
-0.148 343 453 524 72 x 10-1
36
9
2
0.579 229 536 280 84 x 10-3
37
9
26
0.323 089 047 037 11 x 10-2
38
10
0
0.809 648 029 962 15 x 10-4
39
10
1
-0.165 576 797 950 37 x 10-3
40
11
26
-0.449 238 990 618 15 x 10-4

Tutte le proprietà termodinamiche sono derivate dall’equazione (28) con la corretta combinazione degli indici relativi alla energia libera di Helmholtz e relative derivate. Le proprietà più importanti incluso F e relative derivate sono elencati nella tabella 31 mentre tutte le derivate relative all’energia libera di Helmholtz sono elencate nella tabella 32. 

TABELLA 31
Relazioni tra le varie proprietà termodinamiche come da eq. (28)

Proprietà

Relazione

Pressione

Energia specifica interna

Entropia specifica

Entalpia specifica

Capacità termica massica a volume costante

Capacità termica massica a pressione costante

Velocità del suono

Condizione di fase in equilibrio

Legge di Maxwell

TABELLA 32
Relazioni tra le varie proprietà termodinamiche come da eq. (28)

Intervallo di validità

L’equazione (28) è valida per i seguenti valori di temperatura T e pressione p:

623.15 K ≤ T ≤ T(p)eq.(6)

p(T)eq.(5) ≤ p ≤ 100 MPa

Test calcolo computer

La seguente tabella 33 contiene i valori di verifica relativi alla eq. (28).

TABELLA 33
 Valori delle proprietà calcolati con l’eq. (28) in funzione di T e
ρ

 
T = 650 K
ρ = 500 kg·m-3
T = 650 K
ρ = 200 kg·m -3
T = 750 K
ρ = 500 kg·m-3
p (Mpa)
0.255 837 018 x 10²
0.222 930 643 x 102
0.783 095 639 x 102
h (kJ·kg-1)
0.186 343 019 x 104
0.237 512 401 x 104
0.225 868 845 x 104
u (kJ kg-1)
0.181 226 279 x 104
0.226 365 868 x 104
0.210 206 932 x 104
s (kJ·kg-1·K-1)
0.405 427 273 x 101
0.485 438 792 x 101
0.446 971 906 x 101
cp (kJ·kg-1·K-1)
0.138 935 717 x 102
0.446 579 342 x 102
0.634 165 359 x 101
w (m·s-1)
0.502 005 554 x 103
0.383 444 594 x 103
0.760 696 041 x 103